No...it is the Middle Prong of Little River...further west from Greenbriar. If you enter the park on Hwy 73 from Townsend, you make a quick right, towards Cades Cove, then a few hundred yards later, take a left. That is the Tremont road, and the Middle Prong is the stream on your left. The road goes up into the mountains for several miles, the last few as a gravel road, ending in a parking area for the Lynn Camp trail; Lynn Camp is one of two feeder tributaries for the Middle Prong.

They are referring to the Middle of LITTLE RIVER that flows from the left side of the Road as you leave Townsend, and goes up past Tremont Institute. The Middle of LITTLE PIGEON flows through the "Greenbrair Cove" area, One of the Prettiest areas of the Park.
Randy Sale